One of the first problems encountered by every mathematics student starting mathematics education at university is to prove that the square root of two is an irrational number. The reason this question exists is to encourage you to brainstorm and also to open the doors of mathematical thinking to you.
Yes, the square root of 2 is irrational, and, try as you may, you will never be able to write it as a fractional number, a/b, given that a and b are both integers and b≠0.
For example, you can write 0.333… as ⅓ and .123451234512345… as 12345/9999 and √9 as 3. However, regardless of how many digits of √2 you find, you will never be able to write out the entire decimal number, as it follows no determinable pattern and continues infinitely.
The question now is, how can we be so sure? To answer this, I will take you to the story of the Pythagorean Theorem, which you can find my full article on below. As you know, Pythagoras and his students had discovered equations such as a² + b² = c², and they were living out the joy that came with their discoveries.
